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Origins of algebra

Where did the word "Algebra" and its underlying ideas come from? Algebra, a key branch of mathematics, has a rich history. The term 'algebra' comes from an Arabic word meaning 'restoration' or 'completion'. Significant contributions to algebra were made by Diophantus in Greece, Brahmagupta in India, and al-Khwarizmi in Baghdad, who is often credited with giving algebra its name. Created by Sal Khan.

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  • piceratops ultimate style avatar for user DevinLarsen
    At , how does a person or group of people discover/invent a new type of math like Algebra? How did Newton invent calculus? Are there people doing research today creating new math to understand the universe?
    (425 votes)
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    • blobby green style avatar for user sauravshrestha
      How did Newton invent calculus?

      Well, Newton was describing the orbits of planets around the sun, and mentioned that he suspected the orbits were not perfectly circular, but elliptical. A friend colleague of his was unfazed by his assertions.

      "Prove it" said the colleague.

      And Newton shut himself up for two three days trying to come up with a mathematical proof for his theory. He had to invent calculus to do so. Which he did :)
      (420 votes)
  • male robot donald style avatar for user xavier
    Why is algebra so important?
    (133 votes)
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    • male robot hal style avatar for user Severus Snape
      Algebra is important because it is one of the largest, broadest and most relevant type of mathematics today. For an example, we would not be able to have landed on the moon if not for algebra. We would need to substitute unknowns (variables) in place of the information or data we do not have such as the perfect speed of shuttle/spaceship or another variable. Using algebra, constants and what we know for fact, we were able to solve for those variables and launch into space, which was deemed impossible as early as 1000 B.C.
      (209 votes)
  • aqualine sapling style avatar for user Tawnie Isabell Singleton
    What is the difference between Greek letters and Roman letters?
    (39 votes)
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    • leaf green style avatar for user SteveSargentJr
      For the most part, Roman letters are the same letters we use today ( A, B, C, etc.). In contrast, the Ancient Greeks used a different alphabet with different letters and symbols (for instance, when you hear words like "alpha", "beta", and "gamma" you are hearing the names of certain letters in the Greek alphabet). However, the Roman civilization was influenced in a lot of ways by Ancient Greece and, because of that, there were a lot of similarities between the two cultures. As just one example, several of the Roman letters (such as "a" & "b") look a lot like the Greek letters (in this case, "alpha" & "beta").

      In math, you often come across both Roman and Greek letters. For example, when dealing with triangles, you often see the triangle's angles symbolized by Greek letters ("theta" and "phi" are the most commonly used) whereas the sides of the triangle most often have Roman letters for names (such as "a", "b", & "c").

      Hope this helps!
      (76 votes)
  • aqualine ultimate style avatar for user savannah.perkins.2020
    Why is algebra used in our daily lives even if we don't want it to be?
    (25 votes)
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    • leaf red style avatar for user Blaze
      The same reason why the alphabet is used in our daily lives.
      The same reason why you ride in/drive a vehicle every day.
      The same reason why we eat with forks instead of our hands.
      The same reason why a road is called "road".
      The same reason why you usually don't say your middle name.
      The same reason why the numbers on the keyboard I'm typing on are in the order 1 2 3 4 5 6 7 8 9 0.
      The same reason why we store our toothbrushes in the bathroom.
      Et cetera.
      The reason why algebra used in our daily lives even if we don't want it to be is for convenience.
      (Which is the same reason why this post is under "answer" instead of under "comment".)
      Happy Studying!
      (85 votes)
  • duskpin ultimate style avatar for user SavannahFDL
    Why are there multiple fathers of algebra that people credit differently? Sure, the ancient Babylonians could have used Babylonian numerals or something, and the others their form of numbers and symbols, and each person contributed differently. But does algebra have an end? Can we one day, stop discovering more algebraic formulas. Or is algebra this infinite thing that goes on and on and on?
    (16 votes)
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    • duskpin ultimate style avatar for user SherlockHolmes.42
      Great question! I believe that math as a whole is a subject that is constantly expanding as mathematicians discover new laws, formulas, and different ways of looking at math. Algebra is just part of the constantly changing form of math, and so it changes as well over time. Eventually there may be an end to discovering new algebraic formulas, but it will probably take an incredibly long time; and when discovering algebra has come to an end, there will probably be whole new topics of math to study and learn.
      (21 votes)
  • aqualine ultimate style avatar for user (◕‿◕) KarLa Mae (◕‿◕)
    what when can we use algebra in?
    (17 votes)
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  • aqualine ultimate style avatar for user di3goninja300
    I want to become an interpreter (foreign languages are my passion!) Would I ever need to use Algebra in my day-to-day life? If I'm translating words and phrases for someone, aren't numbers universal? Why would I have to learn Algebra if I want to go into a field that deals with spoken language?

    In all my years of school, nobody has ever given me an answer besides "it's required by the state." (I'm in the United States in my Junior year of High School.)
    (8 votes)
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    • mr pink green style avatar for user David Severin
      Math does more than just teach you a bunch of numbers and operations, it helps you do logic, problem solving, and maybe even thinking outside of the box. All these skills could come in handy to any job including interpreter. Plus, what do you mean by interpreter, are you going to work for the State Department, or what? You will have to continue on with Math in college also which is not much better than you have to do it to pass high school.
      (11 votes)
  • male robot hal style avatar for user Abdelrahman Shabasy
    I am a student from egypt who was studying in the national system and now I am preparing for my sat test in order to study abroad in the US. I'm not having any problems in studying english but I am really confused about mathematics I have tried to apply what I have studied in answering the tasks of khan academy but it isn't helping so much so I am confused from where to start.
    (10 votes)
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    • mr pink green style avatar for user David Severin
      Rather than going though Math, you might be better looking at the SAT section of Khan and practice Math (and English there) which has more problems geared toward those that might show up on the SAT. Here in America, our students often take the PSAT in 9th and 10th grade which scores can be linked to Khan to work on areas of weakness, but if you have not done this, studying under the SAT section might be more benificial than doing the math classes.
      (6 votes)
  • blobby green style avatar for user Aaliyah Garrett
    Why was algebra invented in Arabic and when am I going to use algebra in the future?
    (9 votes)
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    • duskpin tree style avatar for user ceevans
      Al-Khwarizmi did all his work in Arabic since he was basing in it the context of 9th-century Arab Abbasid culture. When he wrote his manuscript on mathematics, the world al-jabr was in the title, and the word algebra was derived from it.

      Depending on what career path you choose in life, you could be using algebra every day. Careers based in business, mathematics, computer technology, science, medicine, and architecture and just some examples of jobs where algebra is crucial. Algebra is also used in more mundane activities like budgeting and managing finances or doing taxes.

      Additionally, algebra creates a basis for so much more in math, and all other branches of math use algebra in some way. Learning algebra is one of the most important things you can learn.
      (6 votes)
  • blobby green style avatar for user Erik Hoffman
    I already did all of pre algebra on here. Let the learning begin. I have 125 days to learn this, by verdict of my dad. This will hopefully be a fun challenge.
    (12 votes)
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Video transcript

What I want to do in this video is think about the origins of algebra. The origins of algebra, and the word, especially in association with the ideas that algebra now represents, comes from this book, or actually this is a page of the book right over there. The English translation for the title of this book is the "Compendious Book on Calculation by Completion and Balancing." And it was written by a Persian mathematician who lived in Baghdad in, I believe, it was in the eighth or ninth century. I believe it was actually 820 AD when he wrote this book. AD. And algebra is the Arabic word, that here is the actual title that he gave to it, which is the Arabic title. Algebra means restoration or completion. Restoration or completion. And he associated it in his book with a very specific operation, really taking something from one side of an equation to another side of an equation. But we can actually see it right over here, and I don't know Arabic, but I actually do know some languages that seems to have borrowed a little bit from Arabic, or maybe it went the other way around. But this says Al-kitab, and I know just enough Urdu and Hindi to understand a good India movie, but Al-kitab, kitab means book. So this part is book. Book. Al-mukhtasar, well, I think that means compendious, because I don't know the word for compendious and that seems like that. Fihisab, hisab means calculation in Hindi or Urdu, so this is calculation. Calculation. Al-gabr, this is the root. This is the famous algebra, this is where it shows up. So this is for completion, you could view that as completion. Completion. And then wa'l-muqabala, and that means essentially balancing. Balancing. Completion and balancing. So if we wanted to translate it-- I know this isn't a video on translating Arabic, but the book, I guess this is saying compendious on calculation by completion and balancing is the rough translation right over there. But that is the source of the word algebra, and this is a very, very, very important book. Not just because it was the first use of the word algebra, but many people viewed this book as the first time that algebra took a lot of its modern-- took on many of its modern ideas. Ideas of balancing an equation. The abstract problem itself, not trying to do one off problems here or there. But al-Khwarizmi was not the first person, and just to get an idea of where all this is happening. So he was hanging out in Baghdad, and this part of the world shows up a lot in the history of algebra. But he was hanging out right there in around the eighth or ninth century. So let me draw a time line here, just so we can appreciate everything. So that is timeline, and then whether or not you are religious, most of our modern dates are dependent on the birth of Jesus, so that is right there. Maybe I'll put a cross over there to signify that. When we want to be non-religious, we say the common era. Before the common era, when we want to be religious we say AD, which means in the year of our lord. I don't know the Latin, Anno Domini, I believe, year of our lord. And then when we want-- in the religious context, instead of saying before common era, we say before Christ, BC. But either way, so this is 1000 in the common era. This is 2000 in the common era. And obviously, we are sitting-- at least when I'm making this video, I'm sitting right about there. And then this is 1000 before the common era, and this is 2000 before the common era. So the first traces-- and I'm skipping out, and really, it's just what we can find. I'm sure if we were able to dig more, we might be able to find other evidence of different civilizations and different people stumbling on many of the ideas in algebra. But our first records of people really exploring the ideas that are hit upon in algebra come from ancient Babylon around 2000 years before the common era, before Christ. So right around there there are stone tablets where it looks like people were exploring some of the fundamental ideas of algebra. They weren't using the same symbols. They weren't using the same ways of representing the numbers, but it was algebra that they were working on. And that was, once again, in this part of the world. Babylon was right about there. And Babylon, it's kind of kept the tradition of Sumeria. This whole region was called Mesopotamia, Greek for between two rivers. But that's the first traces of people that we know of that where people were starting to do what we would call real, real algebra. And then you fast forward. And I'm sure we're missing-- and I'm sure even our historians don't know all of the different instances of people using algebra, but the major contributions to algebra, we saw it here in Babylon 2000 years ago. And then if we fast forward to about 200 to 300 AD, so right over there, you have a Greek gentleman who lived in Alexandria. So this is Greece right over here, but he lived in Alexandria, which at the time was part of the Roman Empire. So Alexandria is right over here, and he was a gentleman by the name of Diophantus, or Diophantus. I don't know how to pronounce it, Diophantus. And he is sometimes credited with being the father of algebra, and it's debatable whether it's Diophantus or al-Khwarizmi. al-Khwarizmi, who kind of started using these terms of balancing equations and talking about math in a purer way, while Diophantus was more focused on particular problems. And both of them were kind of beat to the punch by the Babylonians, although they all did contribute in their own way. It's not like they were just copying what the Babylonians did. They had their own unique contributions to what we now consider algebra. But many, especially Western historians, associate Diophantus as the father of algebra. And now, al-Khwarizmi is sometimes what other people would argue as the father of algebra, so he made significant contributions. And if you go to 600 AD-- so if you go to about 600 AD, another famous mathematician in the history of algebra was Brahmagupta, in India. Brahmagupta, in India. So obviously, and actually, I don't know where in India he lived. I should look that up, but roughly in that part of the world. And he also made significant contributions. And then you have al-Khwarizmi, who shows up right there, al-Khwarizmi. And he is the gentleman that definitely we credit with the name algebra, comes from Arabic for restoration, and some people also consider him to be, if not the father of algebra, although some people say he is the father, he is one of the fathers of algebra because he really started to think about algebra in the abstract sense, devoid of some specific problems and a lot of the way a modern mathematician would start to think about the field.